Title :
On Bifurcations of Power Systems at Singularities
Author :
Marszalek, Wieslaw ; Trzaska, Zdzislaw W.
Author_Institution :
DeVry Univ., Brunswick
Abstract :
We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the respective differential-algebraic equations (DAEs) model. In a generic case, the SIB phenomenon in a system of DAEs signals Hopf bifurcation in the singularly perturbed systems of ODEs. The analysis is based on the linear matrix pencil theory and polynomials with parameter dependent coefficients. Several numerical examples are included.
Keywords :
bifurcation; differential algebraic equations; matrix algebra; nonlinear systems; polynomials; power systems; Hopf bifurcation; differential-algebraic equations; linear matrix pencil theory; polynomials; singularity induced bifurcation; singularly perturbed nonlinear power systems; Bifurcation; Eigenvalues and eigenfunctions; Polynomials; Power system analysis computing; Power system control; Power system dynamics; Power system modeling; Power system stability; Power systems; Sufficient conditions; DAEs; Power systems; bifurcations; matrix pencils; singularly perturbed systems;
Conference_Titel :
American Control Conference, 2007. ACC '07
Conference_Location :
New York, NY
Print_ISBN :
1-4244-0988-8
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2007.4282289
